Some photos might help us.
The first thing that I would check is that power is available to all the places it should be when expected. For instance, between B- and pin 12 there should be battery voltage when the FWD control is pressed, and a lower voltage, probably near zero, when it's released.
When running, there has to be a voltage between POT LO and POT HI. That will come out of the controller, but it may only be there when everything else is ready to run. I would expect 5 V or 12 V or similar, but the actual voltage is set by the controller design.
The SPEED LIMIT and POT WIPER voltages should be near the POT LO voltage when the speed limit and throttle respectively are at zero, and should move gradually up to the POT HI voltage when those controls are moved up to their maximum settings.
It doesn't matter if the full voltage range isn't available, as if too little range is available, the top speed and possibly the lowest speed won't be as high or low as expected, but you can fix that later when you get the scooter running.
For instance, when the scooter is ready to run, if you found that the voltage on POT LO is 1 V, and the voltage on POT HI is 5 V, and when the throttle is released, the voltage on POT WIPER is 1.5 V, and pressing the throttle takes that progressively up to 4V, that's would be most likely correct.
If there's never any voltage difference between POT LO and POT HI, disconnect the throttle and the speed limiter from the controller. If there's still no voltage, most likely some switch or fuse or wiring is wrong, but it could be a controller fault. If there is a voltage between POT LO and POT HI with the throttle and the speed limiter disconnected, it is probably a fault in the speed controls.